Event-triggered impulsive control for input-to-state stability of nonlinear time-delay system with delayed impulse.

The problem of input-to-state stability (ISS) was studied in this paper for a class of nonlinear time-delay systems with delayed impulses under event-triggered impulsive control (ETIC), where delays were flexible and external inputs in continuous and impulse dynamics were different. To avoid Zeno behavior, an event-triggered mechanism (ETM) that used the information of the system state and external disturbances was proposed, and the feasibility was enhanced by introducing a forced impulse sequence. Furthermore, some sufficient conditions were formulated to enable ISS for the considered system by using Lyapunov-Razumikhin-like methods. For a class of nonlinear impulse control systems, an application was introduced that utilizes linear matrix inequalities (LMIs) to design an ETM and control gain. Finally, two numerical examples were given to validate the theoretical results.